离散Gross-Pitaevskii方程的涡解
Vortex solutions of the discrete Gross-Pitaevskii equation
摘要：
本文研究了二维散焦离散非线性薛定谔模型中暗涡旋态的动力学演化。我们发现，在某种程度上让人想起他们的一维类似物，即，离散暗孤子的离散散焦涡旋在超过临界耦合强度时变得不稳定，并且在无限晶格中，它们显然保持不稳定直到它们重新稳定的连续极限。在任何无限大晶格中，都可以观察到结构的稳定窗口。系统的工具提供了从连续，特别是从反连续极限的状态的延续。虽然结果主要是面向统一的情况下，我们也考虑了谐波捕获势的影响。
英文摘要：
In this paper, we consider the dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schroedinger model, a model of interest both to atomic physics and to nonlinear optics. We find that in a way reminiscent of their 1d analogs, i.e., of discrete dark solitons, the discrete defocusing vortices become unstable past a critical coupling strength and, in the infinite lattice, they apparently remain unstable up to the continuum limit where they are restabilized. In any infinite lattice, stabilization windows of the structures may be observed. Systematic tools are offered for the continuation of the states both from the continuum and, especially, from the anti-continuum limit. Although the results are mainly geared towards the uniform case, we also consider the effect of harmonic trapping potentials.
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